Moving tasks from one folder to another from the Board view

Some of our team to prefer to work in Board view. Sometimes there is a task on a board that should be in a different folder or project. It would be really useful to be able to drag it from the board to the correct folder in the navigation pane. It looks like you can only drag tasks in to other folders or projects from the list view.

It would be nice not to expect people to have to interrupt their flow by having to change views and then find the task in a list.